Consecutive powers of 3 are added to form this sequence: $3^0,3^0+ 3^1, 3^0+ 3^1+ 3^2$, and so on. What is the simplified value of the fourth term of the sequence?
The fourth term in the sequence is $3^0+3^1+3^2+3^3 = 1+3+9+27 = \boxed{40}$.